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The following are the starting and ending times of activities $A, B, C, D, E, F, G$ and $H$ respectively in chronological order: $“a_s \: b_s \: c_s \: a_e \: d_s \: c_e \: e_s \: f_s \: b_e \: d_e \: g_s \: e_e \: f_e \: h_s \: g_e \: h_e”$. Here, $x_s$ denotes the starting time and $x_e$ denotes the ending time of activity X. We need to schedule the activities in a set of rooms available to us. An activity can be scheduled in a room only if the room is reserved for the activity for its entire duration. What is the minimum number of rooms required?

  1. $3$
  2. $4$
  3. $5$
  4. $6$
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60 votes

Solution: B

The problem can be modeled as a graph coloring problem. Construct a graph with one node corresponding to each activity $A,B,C,D,E,F,G$ and $H$. Connect the activities that occur between the start and end time of an activity. Now, the chromatic number of the graph is the number of rooms required.

17 votes
17 votes

Answer: (B) 

Explanation: Room1 – As
Room2 – Bs
Room3 – As
now A ends (Ae) and now Room3 is free
Room3-Ds
now A ends (Ae) and Room1 is free
Room1-Es
Room4-Fs
now B ends Room2 is free
now D ends Room3 is free
Room2-Gs
now E ends Room1 free
now F ends Room4 free
Room1-Hs
now G and H ends.
Totally used 4 rooms

Source: https://www.gatementor.com/viewtopic.php?f=267&t=2195

Answer:

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